# On PDO in Soccer

## Luck in Sports

In sports analytics (and statistics in general), a great deal of effort goes into determining which phenomena are random, and which are determined by, or predictive of some other piece of information. When trying to determine the skill level of a team, or their ability in a certain area, you want to know whether statistics in this area are indicative of skill itself, or whether or not they are random, undetermined by a team’s true ability. An example here is turnovers in NFL football. It’s been established that, season to season, the turnover margin of a football team is subject to a great deal of randomness. Thus, teams with lower turnover differentials can be considered to be experiencing “bad luck” and be expected to regress toward average luck in the future (with the reverse holding for high differential teams). In soccer, PDO has been put forth as a stat that is an approximate indicator of a team’s “luck”.

The formula for PDO is  PDO = (goals for/shots on target for + (100 – goals against / shots on target against)). The intuition behind PDO as an indicator of luck is that a team which is converting its shots at an unsustainable rate and having its opponents convert at a remarkably low rate is considered lucky. Because of the structure of the stat (each goal scored by one team was a goal against for another), the league average PDO is always 100 (sometimes scaled to 1000). PDO has been shown to revert over the season to a range of approximately 98-102. It would seem then, that PDO gives a good sense of the sustainability of a team’s form.

However, there’s reason to believe that PDO may not be precisely the statistic we want for measuring luck. The article above shows that PDO adjusts over the course of a season, but it doesn’t move to the mean for all teams. Teams which find themselves at the top of the table have consistently higher PDO than those at the bottom. This seems to suggest some kind of relationship between position in the table and PDO, which is worth exploring. It’s also valuable to examine the fundamental assumptions inherent in the formulation of PDO.

## Different Kinds of Shots

Consider the formula for PDO. A higher percentage of converted shots on target (SOT) leads to a higher PDO, as does a lower percentage of opponents SOT converted. Though these effects can be interpreted as luck, as described above, basic intuition about shots suggests a different explanation. The formula for PDO assumes a shot on target from 40 yards is the same as one from 5 yards. Intuitively, this doesn’t seem right. A team taking all of its shots from 40 yards is considered by PDO to be unlucky when it converts these shots at a low rate. I outline two cases of teams whose PDO can be at least partially explained by shot quality.

Arsenal leads the league in PDO through Dec 10. Their SOT conversion percentage has been fairly high over this period, and their SOT against conversion remarkably low. There’s reason to think, however, that these rates are being produced by something other than luck. Colin Trainor at StatsBomb touched on this a few weeks ago, when Arsenal were still on top of the league in terms of PDO. Arsenal are creating an overwhelming majority of their shots from within the penalty area (65% per WhoScored.com). Since these shots are, intuitively, better kinds of shots than those from further away, it lends some support to the idea that Arsenal converting SOTs at a high rate isn’t just down to luck (unless you believe that Arsenal are making these kinds of shots by chance). Similarly, Arsenal’s defensive record reflects that only 46% of the shots they concede come from inside the penalty area (via WhoScored). It seems logical to attribute at least part of Arsenal’s extremely low SOT against conversion to this statistic. If Arsenal are creating good chances, and their defense is effectively limiting the quality of their opponents’ chances, then perhaps Arsenal’s high PDO isn’t down to just luck. Colin Trainor’s article goes into more detail on the ability of a defense to limit shot quality.

Just as Arsenal cast doubt on the “luckiness” of their high PDO, examining shot quality for Tottenham suggests a similar conclusion. Tottenham are an example from the other end of the PDO spectrum. Though their SOT against conversion is better than average, their SOT conversion on offense is by far the lowest in the league, 5 percentage points below lowly Crystal Palace. This can be explained, just as in the case of Arsenal, by looking at the kinds of shots Tottenham is taking. Tottenham’s shots come predominantly from outside the penalty area, with 54% created at that distance. Crystal Palace and Sunderland, the lowest scoring teams in the league, generate 54% and 55% of their shots from outside the box. So, Tottenham’s low SOT conversion rate seems like a product of shot quality more than luck. It could be that Tottenham are converting at lower rates on their long distance shots than other team’s do from similar distances, which would really indicate something more akin to luck, but this isn’t captured  by PDO alone. PDO certainly would be more of an indicator of luck for two teams who are creating similar kinds of chances. But as a league-wide measure of luck, it seems flawed.

In the future it would be interesting to use more detailed shot data to analyze how teams which are creating similar shots fare differently in terms of their conversion. In the meantime, I think PDO as an indicator of luck should be considered only in light of the relevant context of a team’s shooting tendencies.

## Extras

This is my first post on this (or any) blog. I’m hoping to blog about topics in sports analytics as well as posting some of my work in data visualization. I’m currently looking into a space that might better accommodate the static pages I build with for the data viz projects, as well as blog-type content such as this. Currently my data viz projects are hosted on my college web site, and can be found here. Thanks for reading!